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VIII
<br />TAnLu Il.- Radii, Ordinates and Deflections. Chord _100 It.
<br />Deg,
<br />' Radius
<br />Mid.
<br />Ord,
<br />Tan.
<br />Dist,
<br />I Def,
<br />Dist.
<br />I Peffor
<br />1 a t
<br />Deg.
<br />Radios
<br />Mid.
<br />Ord
<br />T...Def.
<br />Dist,
<br />Dist.
<br />boy'
<br />1 Ft.
<br />2° 58, .
<br />t.it.
<br />ror. 15 .
<br />320
<br />181.39
<br />1° 59'
<br />2° 25'
<br />3° to'
<br />t.
<br />.. - t.
<br />fL.
<br />171.01
<br />0'10'
<br />34377,
<br />.036
<br />.145
<br />.291
<br />0:05
<br />7"
<br />8I9.0
<br />1.528
<br />6.105
<br />12.21
<br />2.10
<br />20
<br />17189,
<br />.073
<br />.291
<br />.582
<br />0.10
<br />20'
<br />781.8
<br />1.600
<br />6.395
<br />12.79
<br />2.20
<br />30
<br />11459,
<br />.1.09
<br />.436
<br />.873
<br />0.15
<br />30
<br />764.5
<br />1.637
<br />6.540
<br />13.08
<br />2.25
<br />40
<br />8594.4
<br />•145
<br />.582
<br />1.164
<br />0.20
<br />40
<br />747.9
<br />1.673
<br />6.685
<br />13.37
<br />2.30
<br />50-
<br />'6875.5
<br />.18E
<br />.727
<br />1.454
<br />0.25
<br />8
<br />716.8
<br />1.746
<br />6.976
<br />13.05
<br />2.40
<br />1 -
<br />5729.6
<br />'.218
<br />.873
<br />1.745
<br />0.30
<br />20
<br />688.2
<br />I.619
<br />7.266
<br />14.53
<br />2. i.0
<br />10
<br />4911.2
<br />,255
<br />1.018
<br />2.036
<br />0.35
<br />30
<br />674.7
<br />1.855
<br />7.41L
<br />14.62
<br />2.55
<br />20
<br />'4297.3
<br />.291
<br />1.164
<br />2.327
<br />0.40
<br />40
<br />661.7
<br />1.892
<br />7.556
<br />15.11
<br />2.60
<br />30
<br />3819.8
<br />.327
<br />1.309
<br />2.618
<br />0.45
<br />9
<br />637.3
<br />1.965
<br />7.846
<br />15.69
<br />2.70
<br />40
<br />3137.9
<br />.304
<br />1.454
<br />2.909
<br />0.50
<br />20
<br />614.6
<br />2.037
<br />8.136
<br />16.27
<br />2.80
<br />50
<br />3123.4
<br />.400
<br />1.600
<br />3.200
<br />0.55
<br />30
<br />603.8
<br />2.074
<br />8.281
<br />16.56
<br />2.85
<br />2
<br />2864.9
<br />.436
<br />1.745
<br />3.490
<br />0.60
<br />40
<br />593.4
<br />2.110
<br />8.426
<br />16.85
<br />2.90
<br />10
<br />2644.6
<br />.473
<br />1.891
<br />3.781
<br />0.65
<br />10
<br />573.7
<br />2.183.
<br />8,716
<br />17.43
<br />3.00
<br />20
<br />2155.7
<br />,.509
<br />2.036
<br />4.072
<br />0.70
<br />30
<br />546.4
<br />2.292
<br />9.150
<br />18.30
<br />3.1:5
<br />30
<br />2292.0
<br />.545
<br />2.181
<br />4.363
<br />0.75
<br />11
<br />521.7
<br />2.402
<br />9.585
<br />19.16
<br />3.30
<br />40
<br />2148.8
<br />.582
<br />2.327
<br />4.654
<br />0.80
<br />30
<br />499.1
<br />2.511
<br />10.02
<br />2U.04
<br />3.45
<br />50
<br />2022.4
<br />-.618
<br />2.47 2
<br />4.945
<br />0.85
<br />12.
<br />478.3
<br />2.620
<br />10.45
<br />20.91
<br />3.60
<br />9
<br />1910:1
<br />,.655
<br />2.618
<br />5.235
<br />0.90
<br />30
<br />459.3
<br />2.730
<br />I0.89
<br />21.77
<br />3.75
<br />10
<br />1809.6
<br />.691
<br />2.76 3
<br />5.526
<br />05
<br />.9
<br />13 .
<br />441.7
<br />2.839
<br />11.32
<br />22.64
<br />3.90
<br />20
<br />1719.1
<br />.727
<br />2.908
<br />5.817
<br />1.00
<br />30
<br />425.4
<br />2.949
<br />11.75
<br />23.51
<br />4.05
<br />30
<br />1637.3
<br />.704
<br />3.054
<br />6.108
<br />1.05
<br />14
<br />410.3
<br />3.058,
<br />12.18
<br />24.37
<br />4.20
<br />40
<br />1562.9
<br />.800
<br />3.199
<br />6.398
<br />1.10
<br />30
<br />396.2
<br />19.168
<br />12.62
<br />25.24
<br />4.35
<br />50
<br />1495.0
<br />.836
<br />3.345
<br />6.689
<br />1.15
<br />15
<br />333.1
<br />3.277
<br />13.05
<br />26.11
<br />4.50
<br />4
<br />1132.7
<br />.873
<br />3.490
<br />6.980
<br />1.20
<br />1 30,370.8
<br />3.387
<br />13.49.
<br />26.97
<br />4.65
<br />10
<br />1375:4
<br />'.909
<br />3!635
<br />7.271
<br />1.25
<br />16
<br />359 o3.
<br />3.400
<br />13:92
<br />27.84
<br />4.80
<br />20
<br />1322.5
<br />.945
<br />3.718
<br />7.561
<br />1.30
<br />30
<br />348.5
<br />3.f,06
<br />14235
<br />28,70
<br />4.95
<br />30
<br />1273.6
<br />.982
<br />3.926
<br />7.852
<br />1.35
<br />17
<br />338.3
<br />3.716'14.76
<br />29.56
<br />5.10
<br />40
<br />1228-L
<br />1.018
<br />4.071
<br />8.143
<br />1.40
<br />18
<br />319.6
<br />3.035
<br />15.64
<br />31.29
<br />5.40
<br />50
<br />1185.8
<br />1.055
<br />4.217
<br />8.433
<br />1.45
<br />19
<br />302.9
<br />4.155
<br />16.51
<br />33.01
<br />5.70
<br />5
<br />1146.3
<br />1.091
<br />4.362
<br />8.724
<br />1.50
<br />20
<br />287.9
<br />4-.374
<br />17.37
<br />34.73
<br />6.00
<br />10
<br />1109.3
<br />1.127
<br />4.507
<br />9.014
<br />1.55
<br />21
<br />274.4
<br />4.594
<br />18.22 .36.44
<br />6.30
<br />20
<br />1074.7
<br />1.164
<br />4.653
<br />9.305
<br />1.60
<br />22
<br />262.0
<br />4.81,4
<br />19.08
<br />38.16
<br />6.60
<br />30
<br />1042.1
<br />1.200
<br />4.798
<br />9.596
<br />1.65
<br />23
<br />250.8
<br />5.035
<br />19.94 .39.87
<br />6.90
<br />-CO
<br />1011:5
<br />1.237
<br />4.943
<br />9.886
<br />1.70
<br />24
<br />240.6
<br />5.255
<br />20.79
<br />41.58
<br />7.20
<br />50
<br />982.6
<br />1.273
<br />5.088.10.18
<br />1.75
<br />25
<br />231.0
<br />6.476
<br />21.64
<br />43.28
<br />7.50
<br />6
<br />955.4
<br />1.309
<br />5.234
<br />10.47
<br />1.80
<br />26
<br />222.3
<br />5.697
<br />22.50
<br />44.99
<br />7.80
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />27.
<br />214.2.918
<br />23.35
<br />46.60
<br />8.10
<br />20
<br />905.1
<br />1.382
<br />5.524
<br />11.05
<br />I.90
<br />26
<br />206.7
<br />.139
<br />24.19
<br />48.38
<br />8.40
<br />30
<br />881.9
<br />1.418
<br />5.669
<br />11.34
<br />1.95
<br />29
<br />199.7
<br />6.360
<br />25.04
<br />50.07
<br />8.70
<br />40
<br />859.9
<br />1.455
<br />5.814
<br />11.63
<br />2.00;
<br />30
<br />193.2
<br />6.583
<br />25.88
<br />51.76
<br />9.00
<br />The middle ordinate 'n inches for any cord of length (C) is equal to .0012C1
<br />maltiplied by the lniddTe ordinate taken from the above table. Thus, if it
<br />desired to bond a. 30 ft. rail to fit a 10 degree curve, its middle ordinate should
<br />be .0012X900X2.183 or 2.36 inches.
<br />TABLE III: Deflections for Sub Chords for Short Radius Curves,
<br />Degree ee
<br />Curve
<br />Radius
<br />50
<br />sin. i def.ang.
<br />sub chord
<br />2 R =sin of a def. angle
<br />Length
<br />are
<br />of are
<br />for 100 ft.
<br />12.5 Ft'
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />300
<br />193.18
<br />1° 511
<br />2° 17,
<br />2° 58, .
<br />3° 43'
<br />ror. 15 .
<br />320
<br />181.39
<br />1° 59'
<br />2° 25'
<br />3° to'
<br />3° 58'
<br />tor.33
<br />34°
<br />171.01
<br />2° 06'
<br />2° 33`
<br />3° 21'
<br />4° 12'
<br />to .49
<br />360
<br />161 .8o
<br />2° 13'
<br />2° 41'
<br />3° 33'.
<br />4° 26'
<br />tot .66
<br />380
<br />153.58
<br />20 20'
<br />2° 491
<br />3°44'
<br />4° 40'
<br />101.85
<br />400
<br />146. ig
<br />2.27 1 '
<br />2° 57'
<br />3° 55'
<br />4° 54'
<br />loz. o6
<br />42°
<br />139-52
<br />2:34'
<br />3° 0.5'
<br />4° 07'
<br />5° 08
<br />102.29
<br />44°
<br />133.47
<br />2° 41'
<br />3° 13'
<br />4° 18'
<br />5° 22'
<br />-t02.53
<br />460
<br />127.97.
<br />2° 48'
<br />30 211.
<br />4° 29,
<br />5° 361
<br />102.76
<br />480
<br />122.92
<br />2° 55'
<br />3° 29'
<br />4° 4o'
<br />5° 50'
<br />103.00
<br />50°
<br />118.31
<br />3° 02r
<br />3° 381
<br />4° 51,
<br />_ 6° 04'
<br />103.24
<br />52.°
<br />1114,06
<br />3° 09'
<br />3° 46'
<br />5° 02
<br />6°17'
<br />103. 54
<br />S4°
<br />rt0.11
<br />3° 16'
<br />3° j}'
<br />S° 13'
<br />6° 31'
<br />103.84
<br />56°
<br />106.50
<br />3° 22'
<br />4° 02'
<br />5° 23'
<br />6-44 ,
<br />104.14
<br />58°
<br />103.14
<br />3° 29'
<br />4° lo'
<br />S° 34'
<br />60 47'
<br />104.43
<br />600
<br />100.60
<br />3° 35'
<br />4° 18'
<br />5° 44'
<br />7° 11'
<br />104.72
<br />Ix
<br />CURVE FORMULAS
<br />T= R tan z I R= T cot, 12 I chard'
<br />I = 5o tan 2 I . 50 Chord,def. = K
<br />Sin, i D __
<br />1. 5u R Sin. ; D I
<br />Sin. 11D = No. chords = D
<br />o tan ?
<br />Sin. ' D = a 1, E = T tat, f I Tan. def. = z chord def.
<br />The square of any distance, divided by twice the radius, will equal
<br />1, the distance from tangent to curve, very nearly.
<br />To find angle for a' given distance and deflection.:
<br />1 Rule i. Multiply the given distance by .01746 ((.Ief. for t' for r ft.
<br />see Table II.), and divide "given deflection by the -product.
<br />Rule 2. Multiply given deflection by 57.3, and divide the product by
<br />the given distance.
<br />To find deflection for a given angle and distance. Multiply the angle
<br />by .01745, and the product by the distance.
<br />GENERAL' DATA
<br />RIGHT ANGLE TRIANGLES. Square the altitude, divide by twice the
<br />base. Add quotient to base for hypotenuse. . -
<br />Given. Base too, Alt. 10.10'-' 200=.5. 100+.5-100-,5 hyp>
<br />Given Hyp. roo, Alt. 25.25' 200=3.125. 100-3.125=96.875=Base.
<br />Error in first example, .002 in last, .045.
<br />To find Totts of Rail in one mile of track: inilltiply'weight per yard
<br />by 1 I, and divide by 7.
<br />I..rA°ELIN6. The correction forcurvature and refraction, in feet
<br />and decimals of feet is equal to 0.574d2, where d is the distance in riles.
<br />The correction for curvature alone is closely, ;d2. The. combined cor-
<br />rection is negative.
<br />PROBABLF ERROR. If dl, d2, da, etc. are the discrepancies of various
<br />results from the mean, and if Ede=the sum of the squares of.these differ-
<br />ences and n=the number of observations, then the probable error of the
<br />mean = d2
<br />-0.6745 n (n 1)
<br />SOLAR.EPnEUER1s. Attention.is called to the Solar Ephemeris for
<br />the current year, published by Keuffel & Esser Co., and furnished upon
<br />request. This handy booklet, 3$x6 in., has about 190 pages of data very
<br />useful to the Surveyor; such as the adjustments of transits, levels and solar
<br />attachments; directions and tables for determining the meridian and. the
<br />latiiude from observations on the sun and Polaris; stadia measurements;
<br />magnetic declination; arithmetic constants, etc.
<br />TABLE IV. -Minutes in Decimals of a Degree.
<br />II
<br />.0167
<br />117
<br />.1833
<br />21/
<br />.3500
<br />311
<br />.5167
<br />411
<br />.6833
<br />511
<br />.8500
<br />2
<br />.0333
<br />12
<br />.2000
<br />22
<br />.3667
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />3
<br />.0500
<br />13
<br />.2167
<br />23
<br />.3833
<br />33
<br />.5506
<br />43
<br />.7I67
<br />53
<br />-8833
<br />4
<br />.0667
<br />14
<br />.2333
<br />24
<br />.4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />5
<br />.0933
<br />15 -
<br />.2.500
<br />25
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7:500
<br />55
<br />.9167
<br />6
<br />16
<br />.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />56
<br />:0333.
<br />7
<br />.1000
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />.6167
<br />47
<br />.7833
<br />57
<br />.9fi0o,
<br />8
<br />.11617
<br />.1333
<br />18
<br />.3000
<br />29
<br />.4 fi67
<br />38
<br />.6333
<br />'48
<br />.8000
<br />58
<br />.9667
<br />9
<br />.1500„
<br />19
<br />.3167
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />8167
<br />59
<br />.0833
<br />10
<br />.1667 1
<br />1 29
<br />1 .3333 1
<br />1 30
<br />.5000 1
<br />1 40
<br />.6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />•L%Ri,j. \'.--inches in Decimals of a Fool.
<br />1-I6 3-32jy 3-16-i +5-163`a i 3 ' A
<br />0052 .0078 .0104 .0156 .0208 .0260 I .0313 .0117 I .0a 1 I .06?i 0729
<br />E' 3 '4 5 G f 3 Il 9 `. 10 11 J;
<br />.0833 .1667 .2500 3333 .4167 .5000 .5833 .Gti67 .755. i .9:133 .51167
<br />
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